All language subtitles for 06 - Calculate combinations without duplication

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Would you like to inspect the original subtitles? These are the user uploaded subtitles that are being translated: 1 00:00:00,005 --> 00:00:01,006 - [Instructor] Elsewhere in this course, 2 00:00:01,006 --> 00:00:04,002 I have described how to enumerate 3 00:00:04,002 --> 00:00:07,003 the number of possibilities through permutations 4 00:00:07,003 --> 00:00:10,005 when the order of things matters. 5 00:00:10,005 --> 00:00:12,004 In this movie, I will describe combinations 6 00:00:12,004 --> 00:00:14,005 where order doesn't matter. 7 00:00:14,005 --> 00:00:17,009 As an example, assume that you have five products 8 00:00:17,009 --> 00:00:20,008 and you draw from them to create gift baskets 9 00:00:20,008 --> 00:00:24,000 or samples for potential customers. 10 00:00:24,000 --> 00:00:27,000 So the question is, if you had five items 11 00:00:27,000 --> 00:00:30,004 and you take three, and you do not allow duplication, 12 00:00:30,004 --> 00:00:34,001 how many possible different combinations do you have? 13 00:00:34,001 --> 00:00:38,003 And once again, combinations must occur without duplication. 14 00:00:38,003 --> 00:00:41,001 However, in contrast to permutations, 15 00:00:41,001 --> 00:00:42,005 order doesn't matter. 16 00:00:42,005 --> 00:00:45,006 A gift basket with these three items 17 00:00:45,006 --> 00:00:48,003 would be the same as a gift basket with the same items, 18 00:00:48,003 --> 00:00:52,006 even if they were put into the basket in a different order. 19 00:00:52,006 --> 00:00:56,007 So our goal is to calculate how many unique groups 20 00:00:56,007 --> 00:00:59,004 are possible when choosing three or five products 21 00:00:59,004 --> 00:01:02,001 without allowing repetition. 22 00:01:02,001 --> 00:01:05,003 To demonstrate, I will switch over to Excel. 23 00:01:05,003 --> 00:01:08,002 I have opened this movie's Excel sample file, 24 00:01:08,002 --> 00:01:12,005 and it is 06_06 Combinations Without Duplication. 25 00:01:12,005 --> 00:01:14,004 You can find that in the chapter six folder 26 00:01:14,004 --> 00:01:16,007 of the exercise files collection. 27 00:01:16,007 --> 00:01:18,008 This is a fairly straightforward workbook, 28 00:01:18,008 --> 00:01:22,002 and you can see that I only need two pieces of data, 29 00:01:22,002 --> 00:01:25,002 those are in B-3 and B-4. 30 00:01:25,002 --> 00:01:28,002 Those are the number of available products in B-3, 31 00:01:28,002 --> 00:01:32,007 and the number of items in a sample basket in B-4. 32 00:01:32,007 --> 00:01:34,002 So I'll click in cell B-6, 33 00:01:34,002 --> 00:01:37,003 and I'll create my first formula, 34 00:01:37,003 --> 00:01:39,008 type an equal sign, 35 00:01:39,008 --> 00:01:43,004 and I want to find the number of combinations. 36 00:01:43,004 --> 00:01:46,005 So in other words, because order doesn't matter, 37 00:01:46,005 --> 00:01:51,002 I can use combinations, rather than permutations. 38 00:01:51,002 --> 00:01:54,000 So I'll make sure that I have COMBIN 39 00:01:54,000 --> 00:01:57,001 entered into the formula, 40 00:01:57,001 --> 00:01:59,006 and B-3 contains the number 41 00:01:59,006 --> 00:02:01,009 that is the number of potential items 42 00:02:01,009 --> 00:02:04,003 from which we will select, then a comma, 43 00:02:04,003 --> 00:02:06,001 and the number chosen 44 00:02:06,001 --> 00:02:09,007 that's before the items in each basket. 45 00:02:09,007 --> 00:02:11,004 Write parenthesis and Enter, 46 00:02:11,004 --> 00:02:14,008 and I see that there are 10 possible combinations. 47 00:02:14,008 --> 00:02:17,005 If I increased the number of available products 48 00:02:17,005 --> 00:02:19,009 from five to eight, 49 00:02:19,009 --> 00:02:24,008 we would go from 10 to 56 possible combinations. 50 00:02:24,008 --> 00:02:27,000 And if I wanted to increase the number of items 51 00:02:27,000 --> 00:02:29,004 in the basket from three to four, 52 00:02:29,004 --> 00:02:30,009 still leaving eight available, 53 00:02:30,009 --> 00:02:34,003 we would go from 56 to 70. 54 00:02:34,003 --> 00:02:36,009 Because order doesn't matter with combinations 55 00:02:36,009 --> 00:02:39,002 like it does for permutations, 56 00:02:39,002 --> 00:02:42,006 the number of possible combinations increases more slowly 57 00:02:42,006 --> 00:02:45,007 than does the number of possible permutations. 58 00:02:45,007 --> 00:02:49,000 However, I guarantee that as the number 59 00:02:49,000 --> 00:02:50,001 of available products 60 00:02:50,001 --> 00:02:53,005 and the number of items in the sample basket grow, 61 00:02:53,005 --> 00:02:57,000 the number of combinations will grow very quickly. 4811

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